How to make skin reacting to touch
Final:



You can achieve pretty good effect with Soft Body. I don't know exactly what you want to achieve, but as for deforming skin in general this should be ok.

Mesh:

Default Sphere for Soft Body and Collision. Subdivision Surface is added after (!) Soft Body.



Soft Body:

For Goal you should select Vertex Group marked in previous screenshot or you can even paint Weight for this to mark which part should be affected.

Most important thing is to select Stiff Quads and set Bending > 0.5